Predict Runoff Statistics from Catchment Attributes#
Fig. 9 Example result showing the prediction error after each group of predictors is added, a scatter plot of observed and predicted mean runoff predicted from catchment attributes based on all predictors, the learning curve of training and test sets, and the distribution of target variables.#
Introduction#
We compute the (ordinary) statistics of runoff time series for a large sample of catchments. We then test the predictability of these statistics from catchment attributes using a gradient boosting machine learning approach. The purpose of testing predictability of the order statistics and L-moments is to fully describe parametric distributions for estimating streamflow distributions (flow duration curves), a common problem in applied hydrology.
Catchment attributes are used as predictors of each order statistic. Attributes are added cumulatively in successive tests to compare the contribution of catchment attribute groups related to climate, terrain, land cover, and soil.
We test if transforming the target variable has an effect on the xgboost model. For transformations that do not change the rank of the target variable, i would not expect to see an effect, however the metric used as the objective function may be sensitive to the distribution of target variables, that is sensitive to outliers. We test the predictability of the following:
Statistic |
Description |
|---|---|
|
Mean of the |
|
Median of the |
|
Standard deviation of the |
|
Mean Absolute Deviation (MAD) of the |
|
Mean of the log transformed |
Notes:
uar: unit area runoff is expressed in $L/s/\text{km}^2$.
import os
import pandas as pd
import numpy as np
from pathlib import Path
import xarray as xr
from scipy.stats import skew, kurtosis
from math import comb
from bokeh.plotting import figure, show
from bokeh.layouts import gridplot, row, column
from bokeh.models import HoverTool, ColumnDataSource, Whisker, Legend, LegendItem
from bokeh.transform import factor_cmap, factor_mark
from bokeh.palettes import Category10, Category20, Category20c, Viridis
from bokeh.io import output_notebook
# from bokeh.palettes import Sunset10, Vibrant7
from sklearn.metrics import r2_score
from utils import data_processing_functions as dpf
from scipy.stats import linregress
output_notebook()
BASE_DIR = os.getcwd()
Load Input Data#
# load the catchment characteristics
HYSETS_DIR = Path('/home/danbot/code/common_data/HYSETS')
# load camels hydro attributes to compare with the BCUB data
camels_df = pd.read_csv('data/camels/camels_hydro.txt', sep=';')
camels_df['gauge_id'] = camels_df['gauge_id'].astype(str)
camels_df.head()
hs_df = pd.read_csv('data/HYSETS_watershed_properties.txt', sep=';', dtype={'Watershed_ID': int, 'Official_ID': str})
# create dictionaries for quick lookups
da_dict = {row['Official_ID']: row['Drainage_Area_km2'] for _, row in hs_df.iterrows()}
# needed to map between watershed ID in Hysets data and official_ID
watershed_id_dict = {row['Watershed_ID']: row['Official_ID'] for _, row in hs_df.iterrows()}
# and the inverse
official_id_dict = {row['Official_ID']: row['Watershed_ID'] for _, row in hs_df.iterrows()}
def match_with_padding(oid):
if oid in hs_df['Official_ID'].values:
return oid
print(f'{oid} not found in HYSETS data, trying padded versions...')
for pad in range(1, 4):
padded = oid.zfill(len(oid) + pad)
if padded in hs_df['Official_ID'].values:
print(f' Found padded version: {padded}')
return padded
raise ValueError(f"Official ID {oid} not found in HYSETS data, even with padding.")
Get the watershed attributes file from:
https://doi.org/10.5683/SP3/JNKZVT
# extra stations to exclude (see Notebook 1: Data)
exclude_stations = ['08FA009', '08GA037', '08NC003', '12052500', '12090480', '12107950', '12108450', '12119300',
'12119450', '12200684', '12200762', '12203000', '12409500', '15056070', '15081510',
'12323760', '12143700', '12143900', '12398000', '12058800', '12137800', '12100000']
rev_date = '20250227'
attribute_file = f'BCUB_watershed_attributes_updated_{rev_date}.csv'
updated_attribute_file = 'catchment_attributes_with_runoff_stats.csv'
if not os.path.exists(os.path.join('data', updated_attribute_file)):
print(f'Updated attribute file {updated_attribute_file} not found. Using {attribute_file} instead.')
updated_attribute_path = os.path.join('data', attribute_file)
process_statistics = True
else:
updated_attribute_path = os.path.join(os.getcwd(), 'data', updated_attribute_file)
process_statistics = False
df = pd.read_csv(updated_attribute_path, dtype={'official_id': str})
df['official_id'] = df['official_id'].apply(lambda x: match_with_padding(x))
df = df[~df['official_id'].isin(exclude_stations)]
df = df[[c for c in df.columns if 'unnamed:' not in c.lower()]]
df.columns = [c.lower() for c in df.columns]
df.sort_values('official_id', inplace=True)
df.reset_index(drop=True, inplace=True)
filtered_df = df.copy()
def load_and_filter_hysets_data(station_ids, hs_df):
# load the updated HYSETS data
updated_filename = 'HYSETS_2023_update_QC_stations.nc'
ds = xr.open_dataset(HYSETS_DIR / updated_filename)
# Get valid IDs as a NumPy array
hs_df = hs_df[hs_df['Official_ID'].isin(station_ids)]
selected_ids = hs_df['Watershed_ID'].values
# Get boolean index where watershedID in selected_set
# safely access watershedID as a variable first
ws_ids = ds['watershedID'].data # or .values if you prefer
mask = np.isin(ws_ids, selected_ids)
# Apply mask to data
ds = ds.sel(watershed=mask)
# Step 1: Promote 'watershedID' to a coordinate on the 'watershed' dimension
ds = ds.assign_coords(watershedID=("watershed", ds["watershedID"].data))
# Step 2: Set 'watershedID' as the index for the 'watershed' dimension
return ds.set_index(watershed="watershedID")
def retrieve_timeseries_discharge(stn, ds):
watershed_id = official_id_dict[stn]
# drainage_area = self.ctx.da_dict[stn]
# data = self.ctx.data
da = da_dict[stn]
df = ds['discharge'].sel(watershed=str(watershed_id)).to_dataframe(name='discharge').reset_index()
df = df.set_index('time')[['discharge']]
df.dropna(inplace=True)
# clip minimum flow to 1e-4
df['discharge'] = np.clip(df['discharge'], 1e-4, None)
df.rename(columns={'discharge': stn}, inplace=True)
df[f'{stn}_uar'] = 1000 * df[stn] / da
df[f'{stn}_mm'] = df[stn] * (24 * 3.6 / da)
df['log_x'] = np.log(df[f'{stn}_uar'])
return df
ds = load_and_filter_hysets_data(df['official_id'], hs_df)
target_cols = [
'uar_mean', 'uar_std', 'uar_median', 'uar_mad',
'log_uar_mean', 'log_uar_std', 'log_uar_median', 'log_uar_mad',
]
# target_cols += [f'prob_q_lessthan_{threshold}' for threshold in [1e-4, 5e-4, 1e-3, 5e-3, 1e-2]]
assert np.all([c in filtered_df.columns for c in target_cols]), f"Not all target columns found in filtered df: {target_cols} \n {list(df.columns)}"
from bokeh.models import ColorBar, LogColorMapper, ColumnDataSource
# visualize the distribution of the mean runoff
p1 = figure(title="Mean runoff distribution", width=500, height=300)
hist, edges = np.histogram(filtered_df['uar_mean'], density=True, bins=50)
p1.quad(top=hist, bottom=0, left=edges[:-1], right=edges[1:], line_color='white')
p1.xaxis.axis_label = 'Mean runoff [L/s/km^2]'
p1.yaxis.axis_label = 'Frequency'
# visualize a scatter plot of the mean and standard deviation
p2 = figure(title=f"Mean vs. Standard deviation (N={len(df)})", width=500, height=300)
# add color mapper to encode drainage_area_km2
mapper = LogColorMapper(palette='Viridis256', low=filtered_df['drainage_area_km2'].min(),
high=filtered_df['drainage_area_km2'].max())
source = ColumnDataSource(filtered_df)
color_bar = ColorBar(color_mapper=mapper, width=8, location=(0,0), title='Drainage area [km²]',)
p2.add_layout(color_bar, 'right')
# add the scatter plot with color mapping
p2.scatter('uar_mean', 'uar_std', source=source, color={'field': 'drainage_area_km2', 'transform': mapper})
x = np.linspace(0, filtered_df['uar_mean'].max(), 100)
slope, intercept, r, pval, se = linregress(filtered_df['uar_mean'].values, filtered_df['uar_std'].values)
y = [slope*e + intercept for e in x]
p2.line(x, y, legend_label=f'L2: y={slope:.2f}x + {intercept:.2f} (R²={r**2:.2f})',
line_width=2, color='red', line_dash='dashed')
# plot the L1 Norm -- L2 is sensitive to outliers and is biased for low mean values
# l1_slope, l1_intercept = L1_fit_line(df['mean_uar'].values, df['sd_uar'].values)
# yl1 = [l1_slope*e + l1_intercept for e in x]
# p2.line(x, yl1, legend_label=f'L1: y={l1_slope:.2f}x + {l1_intercept:.2f}',
# line_width=2, color='red', line_dash='dotted')
p2.line([0, filtered_df['uar_mean'].max()], [0, filtered_df['uar_mean'].max()],
line_width=2, color='black', line_dash='dotted', legend_label='1:1')
# add hover tool to show official_id
p2.add_tools(HoverTool(tooltips=[('Official ID', '@official_id')]))
# p2.xaxis.axis_label = 'Mean runoff [mm/day]'
p2.xaxis.axis_label = 'Mean runoff [L/s/km^2]'
p2.yaxis.axis_label = 'Standard deviation'
p2.legend.location = 'top_left'
p2.legend.background_fill_alpha = 0.5
p2.legend.click_policy = 'hide'
show(row(p1, p2))
Define attribute groups#
terrain = ['drainage_area_km2', 'elevation_m', 'slope_deg', 'aspect_deg']
land_cover = [
'land_use_forest_frac_2010', 'land_use_grass_frac_2010', 'land_use_wetland_frac_2010', 'land_use_water_frac_2010',
'land_use_urban_frac_2010', 'land_use_shrubs_frac_2010', 'land_use_crops_frac_2010', 'land_use_snow_ice_frac_2010']
climate = ['prcp', 'srad', 'swe', 'tmax', 'tmin', 'vp', 'high_prcp_freq', 'high_prcp_duration', 'low_prcp_freq', 'low_prcp_duration']
soil = ['logk_ice_x100', 'porosity_x100']
all_attributes = terrain + land_cover + soil + climate
assert len([c for c in all_attributes if c not in df.columns]) == 0
len(all_attributes)
24
results_folder = os.path.join(BASE_DIR, 'data', 'results', 'parameter_prediction_results')
if not os.path.exists(results_folder):
os.makedirs(results_folder)
nfolds = 5
n_boost_rounds = 500
n_optimization_rounds = 20
loss = 'reg:squarederror'
# loss = 'reg:absoluteerror'
all_test_results = {}
attribute_set_dict = {
'climate': climate,
'+land_cover': land_cover,
'+terrain': terrain,
'+soil': soil,
}
Set Attribute Groupings#
group_1 = ['climate', '+terrain', '+land_cover', '+soil']
# for group 2, just reverse group 1
group_2 = group_1[::-1]
group_3 = ['+land_cover', '+terrain', '+soil', 'climate']
group_4 = ['+soil', 'climate', '+land_cover', '+terrain']
attribute_group_orders = [group_1, group_2, group_3, group_4]
Run XGBoost Models#
Separate the test set at the outset so the attribute group ordering is tested on the same hold-out set but necessarily on unique training optimizations. This ensures that at least the presence of outliers in the hold-out set should at least be constant across the attribute group reordering.
from utils.xgb_functions import run_xgb_CV_trials
def predict_runoff_from_attributes(df, target_column, group_order, results_folder, n_boost_rounds, n_optimization_rounds, loss):
"""
Note that here we're predicting the log mean unit area runoff
"""
# set the target column
predictor_attributes = []
results = {}
# add attribute groups successively
for set_name in group_order:
print(f' Processing {set_name} attribute set')
predictor_attributes += attribute_set_dict[set_name]
input_data = df[['official_id'] + predictor_attributes + [target_column]].copy()
result_df, all_predictions_df, all_convergence_df = run_xgb_CV_trials(
set_name, predictor_attributes, target_column, input_data,
n_optimization_rounds, nfolds, n_boost_rounds, results_folder,
loss=loss,
)
# store the test set predictions and actuals
results[set_name] = {
'all_results': result_df,
'convergence': all_convergence_df,
'oos_predictions': all_predictions_df,
}
return results
results_dict = {}
group_results_dict = {}
eval_metrics = {'reg:squarederror': 'test_rmse', 'reg:absoluteerror': 'test_mae'}
for target_col in target_cols:
n = 0
min_error = 1e9
best_set = None
results_dict[target_col] = {}
group_results_dict[target_col] = {}
print(f'TARGET: {target_col}')
eval_metric = eval_metrics[loss]
for n, group in enumerate(attribute_group_orders):
print(f'Processing: {group} ordering. {n}/{len(attribute_group_orders)}.')
group_results_fname = f'{target_col}_prediction_results_{"".join(group)}.npy'
group_results_fpath = os.path.join(results_folder, group_results_fname)
print(f'Group results file: {group_results_fpath}')
if os.path.exists(group_results_fpath):
print(f'Retrieving existing results from {group_results_fpath}')
group_results = np.load(group_results_fpath, allow_pickle=True).item()
else:
group_results = predict_runoff_from_attributes(filtered_df, target_col, group, results_folder, n_boost_rounds, n_optimization_rounds, loss)
np.save(group_results_fpath, group_results)
group_results_dict[target_col][n] = {'order': group, 'results': group_results}
for k, test_data in group_results.items():
# Save all results, not just the best
results_dict[target_col][f'group_{n}'] = {
'group_order': group,
'test_error': test_data['all_results'][f'{eval_metric}_mean'],
'test_error_std': test_data['all_results'][f'{eval_metric}_stdev'],
'convergence': test_data['convergence'],
'oos_predictions': test_data['oos_predictions'],
}
# print(f'Group {n} {k} {eval_metric}: {results_dict[target_col][f"group_{n}"]["test_error"]}')
summary_csv = f'{target_col}_summary_group_{n}.csv'
test_data['oos_predictions'].to_csv(os.path.join(results_folder, summary_csv), index=False)
TARGET: uar_mean
Processing: ['climate', '+terrain', '+land_cover', '+soil'] ordering. 0/4.
Group results file: /home/danbot/code/distribution_estimation/docs/notebooks/data/results/parameter_prediction_results/uar_mean_prediction_results_climate+terrain+land_cover+soil.npy
Retrieving existing results from /home/danbot/code/distribution_estimation/docs/notebooks/data/results/parameter_prediction_results/uar_mean_prediction_results_climate+terrain+land_cover+soil.npy
Processing: ['+soil', '+land_cover', '+terrain', 'climate'] ordering. 1/4.
Group results file: /home/danbot/code/distribution_estimation/docs/notebooks/data/results/parameter_prediction_results/uar_mean_prediction_results_+soil+land_cover+terrainclimate.npy
Retrieving existing results from /home/danbot/code/distribution_estimation/docs/notebooks/data/results/parameter_prediction_results/uar_mean_prediction_results_+soil+land_cover+terrainclimate.npy
Processing: ['+land_cover', '+terrain', '+soil', 'climate'] ordering. 2/4.
Group results file: /home/danbot/code/distribution_estimation/docs/notebooks/data/results/parameter_prediction_results/uar_mean_prediction_results_+land_cover+terrain+soilclimate.npy
Retrieving existing results from /home/danbot/code/distribution_estimation/docs/notebooks/data/results/parameter_prediction_results/uar_mean_prediction_results_+land_cover+terrain+soilclimate.npy
Processing: ['+soil', 'climate', '+land_cover', '+terrain'] ordering. 3/4.
Group results file: /home/danbot/code/distribution_estimation/docs/notebooks/data/results/parameter_prediction_results/uar_mean_prediction_results_+soilclimate+land_cover+terrain.npy
Retrieving existing results from /home/danbot/code/distribution_estimation/docs/notebooks/data/results/parameter_prediction_results/uar_mean_prediction_results_+soilclimate+land_cover+terrain.npy
TARGET: uar_std
Processing: ['climate', '+terrain', '+land_cover', '+soil'] ordering. 0/4.
Group results file: /home/danbot/code/distribution_estimation/docs/notebooks/data/results/parameter_prediction_results/uar_std_prediction_results_climate+terrain+land_cover+soil.npy
Retrieving existing results from /home/danbot/code/distribution_estimation/docs/notebooks/data/results/parameter_prediction_results/uar_std_prediction_results_climate+terrain+land_cover+soil.npy
Processing: ['+soil', '+land_cover', '+terrain', 'climate'] ordering. 1/4.
Group results file: /home/danbot/code/distribution_estimation/docs/notebooks/data/results/parameter_prediction_results/uar_std_prediction_results_+soil+land_cover+terrainclimate.npy
Retrieving existing results from /home/danbot/code/distribution_estimation/docs/notebooks/data/results/parameter_prediction_results/uar_std_prediction_results_+soil+land_cover+terrainclimate.npy
Processing: ['+land_cover', '+terrain', '+soil', 'climate'] ordering. 2/4.
Group results file: /home/danbot/code/distribution_estimation/docs/notebooks/data/results/parameter_prediction_results/uar_std_prediction_results_+land_cover+terrain+soilclimate.npy
Retrieving existing results from /home/danbot/code/distribution_estimation/docs/notebooks/data/results/parameter_prediction_results/uar_std_prediction_results_+land_cover+terrain+soilclimate.npy
Processing: ['+soil', 'climate', '+land_cover', '+terrain'] ordering. 3/4.
Group results file: /home/danbot/code/distribution_estimation/docs/notebooks/data/results/parameter_prediction_results/uar_std_prediction_results_+soilclimate+land_cover+terrain.npy
Retrieving existing results from /home/danbot/code/distribution_estimation/docs/notebooks/data/results/parameter_prediction_results/uar_std_prediction_results_+soilclimate+land_cover+terrain.npy
TARGET: uar_median
Processing: ['climate', '+terrain', '+land_cover', '+soil'] ordering. 0/4.
Group results file: /home/danbot/code/distribution_estimation/docs/notebooks/data/results/parameter_prediction_results/uar_median_prediction_results_climate+terrain+land_cover+soil.npy
Retrieving existing results from /home/danbot/code/distribution_estimation/docs/notebooks/data/results/parameter_prediction_results/uar_median_prediction_results_climate+terrain+land_cover+soil.npy
Processing: ['+soil', '+land_cover', '+terrain', 'climate'] ordering. 1/4.
Group results file: /home/danbot/code/distribution_estimation/docs/notebooks/data/results/parameter_prediction_results/uar_median_prediction_results_+soil+land_cover+terrainclimate.npy
Retrieving existing results from /home/danbot/code/distribution_estimation/docs/notebooks/data/results/parameter_prediction_results/uar_median_prediction_results_+soil+land_cover+terrainclimate.npy
Processing: ['+land_cover', '+terrain', '+soil', 'climate'] ordering. 2/4.
Group results file: /home/danbot/code/distribution_estimation/docs/notebooks/data/results/parameter_prediction_results/uar_median_prediction_results_+land_cover+terrain+soilclimate.npy
Retrieving existing results from /home/danbot/code/distribution_estimation/docs/notebooks/data/results/parameter_prediction_results/uar_median_prediction_results_+land_cover+terrain+soilclimate.npy
Processing: ['+soil', 'climate', '+land_cover', '+terrain'] ordering. 3/4.
Group results file: /home/danbot/code/distribution_estimation/docs/notebooks/data/results/parameter_prediction_results/uar_median_prediction_results_+soilclimate+land_cover+terrain.npy
Retrieving existing results from /home/danbot/code/distribution_estimation/docs/notebooks/data/results/parameter_prediction_results/uar_median_prediction_results_+soilclimate+land_cover+terrain.npy
TARGET: uar_mad
Processing: ['climate', '+terrain', '+land_cover', '+soil'] ordering. 0/4.
Group results file: /home/danbot/code/distribution_estimation/docs/notebooks/data/results/parameter_prediction_results/uar_mad_prediction_results_climate+terrain+land_cover+soil.npy
Retrieving existing results from /home/danbot/code/distribution_estimation/docs/notebooks/data/results/parameter_prediction_results/uar_mad_prediction_results_climate+terrain+land_cover+soil.npy
Processing: ['+soil', '+land_cover', '+terrain', 'climate'] ordering. 1/4.
Group results file: /home/danbot/code/distribution_estimation/docs/notebooks/data/results/parameter_prediction_results/uar_mad_prediction_results_+soil+land_cover+terrainclimate.npy
Retrieving existing results from /home/danbot/code/distribution_estimation/docs/notebooks/data/results/parameter_prediction_results/uar_mad_prediction_results_+soil+land_cover+terrainclimate.npy
Processing: ['+land_cover', '+terrain', '+soil', 'climate'] ordering. 2/4.
Group results file: /home/danbot/code/distribution_estimation/docs/notebooks/data/results/parameter_prediction_results/uar_mad_prediction_results_+land_cover+terrain+soilclimate.npy
Retrieving existing results from /home/danbot/code/distribution_estimation/docs/notebooks/data/results/parameter_prediction_results/uar_mad_prediction_results_+land_cover+terrain+soilclimate.npy
Processing: ['+soil', 'climate', '+land_cover', '+terrain'] ordering. 3/4.
Group results file: /home/danbot/code/distribution_estimation/docs/notebooks/data/results/parameter_prediction_results/uar_mad_prediction_results_+soilclimate+land_cover+terrain.npy
Retrieving existing results from /home/danbot/code/distribution_estimation/docs/notebooks/data/results/parameter_prediction_results/uar_mad_prediction_results_+soilclimate+land_cover+terrain.npy
TARGET: log_uar_mean
Processing: ['climate', '+terrain', '+land_cover', '+soil'] ordering. 0/4.
Group results file: /home/danbot/code/distribution_estimation/docs/notebooks/data/results/parameter_prediction_results/log_uar_mean_prediction_results_climate+terrain+land_cover+soil.npy
Retrieving existing results from /home/danbot/code/distribution_estimation/docs/notebooks/data/results/parameter_prediction_results/log_uar_mean_prediction_results_climate+terrain+land_cover+soil.npy
Processing: ['+soil', '+land_cover', '+terrain', 'climate'] ordering. 1/4.
Group results file: /home/danbot/code/distribution_estimation/docs/notebooks/data/results/parameter_prediction_results/log_uar_mean_prediction_results_+soil+land_cover+terrainclimate.npy
Retrieving existing results from /home/danbot/code/distribution_estimation/docs/notebooks/data/results/parameter_prediction_results/log_uar_mean_prediction_results_+soil+land_cover+terrainclimate.npy
Processing: ['+land_cover', '+terrain', '+soil', 'climate'] ordering. 2/4.
Group results file: /home/danbot/code/distribution_estimation/docs/notebooks/data/results/parameter_prediction_results/log_uar_mean_prediction_results_+land_cover+terrain+soilclimate.npy
Retrieving existing results from /home/danbot/code/distribution_estimation/docs/notebooks/data/results/parameter_prediction_results/log_uar_mean_prediction_results_+land_cover+terrain+soilclimate.npy
Processing: ['+soil', 'climate', '+land_cover', '+terrain'] ordering. 3/4.
Group results file: /home/danbot/code/distribution_estimation/docs/notebooks/data/results/parameter_prediction_results/log_uar_mean_prediction_results_+soilclimate+land_cover+terrain.npy
Retrieving existing results from /home/danbot/code/distribution_estimation/docs/notebooks/data/results/parameter_prediction_results/log_uar_mean_prediction_results_+soilclimate+land_cover+terrain.npy
TARGET: log_uar_std
Processing: ['climate', '+terrain', '+land_cover', '+soil'] ordering. 0/4.
Group results file: /home/danbot/code/distribution_estimation/docs/notebooks/data/results/parameter_prediction_results/log_uar_std_prediction_results_climate+terrain+land_cover+soil.npy
Retrieving existing results from /home/danbot/code/distribution_estimation/docs/notebooks/data/results/parameter_prediction_results/log_uar_std_prediction_results_climate+terrain+land_cover+soil.npy
Processing: ['+soil', '+land_cover', '+terrain', 'climate'] ordering. 1/4.
Group results file: /home/danbot/code/distribution_estimation/docs/notebooks/data/results/parameter_prediction_results/log_uar_std_prediction_results_+soil+land_cover+terrainclimate.npy
Retrieving existing results from /home/danbot/code/distribution_estimation/docs/notebooks/data/results/parameter_prediction_results/log_uar_std_prediction_results_+soil+land_cover+terrainclimate.npy
Processing: ['+land_cover', '+terrain', '+soil', 'climate'] ordering. 2/4.
Group results file: /home/danbot/code/distribution_estimation/docs/notebooks/data/results/parameter_prediction_results/log_uar_std_prediction_results_+land_cover+terrain+soilclimate.npy
Retrieving existing results from /home/danbot/code/distribution_estimation/docs/notebooks/data/results/parameter_prediction_results/log_uar_std_prediction_results_+land_cover+terrain+soilclimate.npy
Processing: ['+soil', 'climate', '+land_cover', '+terrain'] ordering. 3/4.
Group results file: /home/danbot/code/distribution_estimation/docs/notebooks/data/results/parameter_prediction_results/log_uar_std_prediction_results_+soilclimate+land_cover+terrain.npy
Retrieving existing results from /home/danbot/code/distribution_estimation/docs/notebooks/data/results/parameter_prediction_results/log_uar_std_prediction_results_+soilclimate+land_cover+terrain.npy
TARGET: log_uar_median
Processing: ['climate', '+terrain', '+land_cover', '+soil'] ordering. 0/4.
Group results file: /home/danbot/code/distribution_estimation/docs/notebooks/data/results/parameter_prediction_results/log_uar_median_prediction_results_climate+terrain+land_cover+soil.npy
Retrieving existing results from /home/danbot/code/distribution_estimation/docs/notebooks/data/results/parameter_prediction_results/log_uar_median_prediction_results_climate+terrain+land_cover+soil.npy
Processing: ['+soil', '+land_cover', '+terrain', 'climate'] ordering. 1/4.
Group results file: /home/danbot/code/distribution_estimation/docs/notebooks/data/results/parameter_prediction_results/log_uar_median_prediction_results_+soil+land_cover+terrainclimate.npy
Retrieving existing results from /home/danbot/code/distribution_estimation/docs/notebooks/data/results/parameter_prediction_results/log_uar_median_prediction_results_+soil+land_cover+terrainclimate.npy
Processing: ['+land_cover', '+terrain', '+soil', 'climate'] ordering. 2/4.
Group results file: /home/danbot/code/distribution_estimation/docs/notebooks/data/results/parameter_prediction_results/log_uar_median_prediction_results_+land_cover+terrain+soilclimate.npy
Retrieving existing results from /home/danbot/code/distribution_estimation/docs/notebooks/data/results/parameter_prediction_results/log_uar_median_prediction_results_+land_cover+terrain+soilclimate.npy
Processing: ['+soil', 'climate', '+land_cover', '+terrain'] ordering. 3/4.
Group results file: /home/danbot/code/distribution_estimation/docs/notebooks/data/results/parameter_prediction_results/log_uar_median_prediction_results_+soilclimate+land_cover+terrain.npy
Retrieving existing results from /home/danbot/code/distribution_estimation/docs/notebooks/data/results/parameter_prediction_results/log_uar_median_prediction_results_+soilclimate+land_cover+terrain.npy
TARGET: log_uar_mad
Processing: ['climate', '+terrain', '+land_cover', '+soil'] ordering. 0/4.
Group results file: /home/danbot/code/distribution_estimation/docs/notebooks/data/results/parameter_prediction_results/log_uar_mad_prediction_results_climate+terrain+land_cover+soil.npy
Retrieving existing results from /home/danbot/code/distribution_estimation/docs/notebooks/data/results/parameter_prediction_results/log_uar_mad_prediction_results_climate+terrain+land_cover+soil.npy
Processing: ['+soil', '+land_cover', '+terrain', 'climate'] ordering. 1/4.
Group results file: /home/danbot/code/distribution_estimation/docs/notebooks/data/results/parameter_prediction_results/log_uar_mad_prediction_results_+soil+land_cover+terrainclimate.npy
Retrieving existing results from /home/danbot/code/distribution_estimation/docs/notebooks/data/results/parameter_prediction_results/log_uar_mad_prediction_results_+soil+land_cover+terrainclimate.npy
Processing: ['+land_cover', '+terrain', '+soil', 'climate'] ordering. 2/4.
Group results file: /home/danbot/code/distribution_estimation/docs/notebooks/data/results/parameter_prediction_results/log_uar_mad_prediction_results_+land_cover+terrain+soilclimate.npy
Retrieving existing results from /home/danbot/code/distribution_estimation/docs/notebooks/data/results/parameter_prediction_results/log_uar_mad_prediction_results_+land_cover+terrain+soilclimate.npy
Processing: ['+soil', 'climate', '+land_cover', '+terrain'] ordering. 3/4.
Group results file: /home/danbot/code/distribution_estimation/docs/notebooks/data/results/parameter_prediction_results/log_uar_mad_prediction_results_+soilclimate+land_cover+terrain.npy
Retrieving existing results from /home/danbot/code/distribution_estimation/docs/notebooks/data/results/parameter_prediction_results/log_uar_mad_prediction_results_+soilclimate+land_cover+terrain.npy
label_dict = {
'uar_mean': {'x': r'$$\mu_i \left[ L s^{-1} \text{km}^{-2}\right]$$', 'y': r'$$\hat \mu_i \left[L s^{-1} \text{km}^{-2} \right]$$'},
'uar_std': {'x': r'$$\sigma_i \left[ L s^{-1} \text{km}^{-2}\right]$$', 'y': r'$$\hat \sigma_i \left[ L s^{-1} \text{km}^{-2} \right]$$'},
'uar_median': {'x': r'$$\text{Median}_i \left[ L s^{-1} \text{km}^{-2}\right]$$', 'y': r'$$ \text{Median}_\text{est} \left[ L s^{-1} \text{km}^{-2} \right]$$'},
'uar_mad': {'x': r'$$\text{MAD}_i \left[ L s^{-1} \text{km}^{-2}\right]$$', 'y': r'$$\text{MAD}_\text{est} \left[ L s^{-1} \text{km}^{-2} \right]$$'},
'log_uar_mean': {'x': r'$$\log \mu \left[ L s^{-1} \text{km}^{-2} \right]$$', 'y': r'$$ \log \hat \mu \left[ L s^{-1} \text{km}^{-2} \right]$$'},
'log_uar_median': {'x': r'$$\log \text{Median} \left[ L s^{-1} \text{km}^{-2} \right]$$', 'y': r'$$ \text{Log Median}_\text{est} \left[ L s^{-1} \text{km}^{-2} \right]$$'},
'log_uar_std': {'x': r'$$\log\ \sigma_i \left[ L s^{-1} \text{km}^{-2} \right]$$', 'y': r'$$\log \hat \sigma_i \left[ L s^{-1} \text{km}^{-2} \right]$$'},
'log_uar_mad': {'x': r'$$\log\ \text{MAD}_i \left[ L s^{-1} \text{km}^{-2} \right]$$', 'y': r'$$ \text{Log MAD}_\text{est} \left[ L s^{-1} \text{km}^{-2} \right]$$'},
}
target_cols = [
'uar_mean', 'uar_std', 'uar_median', 'uar_mad',
'log_uar_mean', 'log_uar_std', 'log_uar_median', 'log_uar_mad',
]
View Results#
def create_results_plots(target_col, results_df, attribute_sets, eval_metric, title=''):
plots = []
def _plot_attribute_order_line():
means, lbs, ubs = [], [], []
for e in attribute_sets:
df = results_df[e]['all_results']
trial_means = df[f'{eval_metric}_mean'].values
means.append(np.mean(trial_means))
lb, ub = np.percentile(trial_means, [2.5, 97.5])
lbs.append(lb)
ubs.append(ub)
max_range = (0.95*min(lbs), max(ubs)*1.05)
group_order = [e if not e.startswith('+') else e[1:] for e in attribute_sets]
group_order = group_order[:1] + [f'+{e}' for e in group_order[1:]] # add '+' to all but the first element
source = ColumnDataSource({'x': group_order, 'y1': means, 'ub': ubs, 'lb': lbs})
fig = figure(title='', x_range=group_order, y_range=max_range)#y_range=max_range)
fig.scatter('x', 'y1', legend_label=eval_metric.upper(), color='green', source=source, line_width=3, marker='square', size=4)
fig.add_layout(Whisker(source=source, base='x', upper='ub', lower='lb', line_width=1))
fig.legend.background_fill_alpha = 0.6
fig.yaxis.axis_label = r'$$\text{RMSE}$$'
fig.xaxis.axis_label = r'$$\text{Attribute Groups}$$'
best_set = min(attribute_sets, key=lambda x: results_df[x]['all_results'][f'{eval_metric}_mean'].mean())
return fig, best_set
def _plot_scatter_with_regression(best_result_df, xlabel, ylabel, target_col):
trial_r2 = (
best_result_df.groupby('trial')[['actual', 'predicted']]
.apply(lambda df: r2_score(df['actual'], df['predicted']))
)
# r2_mean = trial_r2.mean()
r2_std = trial_r2.std()
grouped = best_result_df.groupby('trial').agg({
'actual': 'median',
'predicted': 'median',
})
grouped['diff'] = (grouped['actual'] - grouped['predicted']).abs()
median_trial = grouped.sort_values('diff').index[len(grouped) // 2]
median_result = best_result_df[best_result_df['trial'] == median_trial].copy()
xx, yy = median_result['actual'].values, median_result['predicted'].values
source = ColumnDataSource({'x': xx, 'y': yy, 'ID': median_result['official_id'].values})
slope, intercept, r, p, se = linregress(xx, yy)
sfig = figure(title='')
sfig.scatter('x', 'y', size=3, alpha=0.8, source=source, legend_label=target_col, color='blue')
sfig.add_tools(HoverTool(tooltips=[('ID', '@ID')]))
x_obs = np.linspace(min(xx), max(xx), 1000)
ybf = [slope * e + intercept for e in x_obs]
sfig.line(x_obs, ybf, color='red', line_width=3, line_dash='dashed', legend_label=f'R²={r**2:.2f} ± {r2_std:.3f}')
sfig.line([0, max(ybf)], [0, max(ybf)], color='black', line_dash='dotted', line_width=2, legend_label='1:1')
sfig.xaxis.axis_label = xlabel
sfig.yaxis.axis_label = ylabel
sfig.legend.background_fill_alpha = 0.5
sfig.legend.location = 'top_left'
return sfig, median_trial
def _plot_convergence(convergence_df, median_trial):
cfig = figure(title='')
data = convergence_df[convergence_df['trial'] == median_trial].copy()
fold_nos = sorted(set(convergence_df['fold']))
min_pred_risk = 1e9
for fn in fold_nos:
fold_data = data[data['fold'] == fn].copy()
cfig.line(fold_data['round'], fold_data[f'test'], line_alpha=0.6, line_color='red', line_dash='dotted', legend_label=f'Test Folds')
cfig.line(fold_data['round'], fold_data[f'train'], line_alpha=0.7, line_color='grey', line_dash='dotted', legend_label=f'Train Folds')
train_pivot = data.pivot_table(index='round', columns='fold', values='train')#, aggfunc='first')
test_pivot = data.pivot_table(index='round', columns='fold', values='test')#, aggfunc='first')
train_pivot.columns = [f'fold_{col}' for col in train_pivot.columns]
test_pivot.columns = [f'fold_{col}' for col in test_pivot.columns]
train_pivot['mean'] = train_pivot.mean(axis=1)
test_pivot['mean'] = test_pivot.mean(axis=1)
cfig.line(train_pivot.index, train_pivot['mean'], line_alpha=0.5, line_color='grey', line_width=2, legend_label='CV Mean (Train)')
cfig.line(test_pivot.index, test_pivot['mean'], line_alpha=0.5, line_color='red', line_width=2, legend_label='CV Mean (Test)')
min_pred_risk_idx = test_pivot['mean'].idxmin()
min_pred_risk = test_pivot.loc[min_pred_risk_idx, 'mean']
if min_pred_risk_idx == max(test_pivot['mean'].index):
print(f'Min prediction risk occurs at the maximum iteration, try increasing the number of boosting rounds')
cfig.line([min_pred_risk_idx, min_pred_risk_idx], [0, min_pred_risk], legend_label='Min risk', color='green', line_width=2, line_dash='dashed')
cfig.legend.location = 'top_right'
cfig.legend.background_fill_alpha = 0.5
cfig.xaxis.axis_label = r'$$\text{Iteration}$$'
cfig.yaxis.axis_label = r'$$\text{RMSE}$$'
return cfig
def _plot_target_cdfs(cdf_arrays, xlabel):
cdffig = figure(title='', x_axis_type='log')
for (cdfx, cdfy) in cdf_arrays:
cdffig.line(cdfx, cdfy, color='black', line_alpha=0.6, line_width=2, legend_label='Fold CDFs')
cdffig.xaxis.axis_label = xlabel
cdffig.yaxis.axis_label = r'$$\text{Pr}(X\leq x) $$'
cdffig.legend.location = 'top_left'
return cdffig
def _compute_empirical_cdf(data):
sorted_data = np.sort(data)
cdf = np.arange(1, len(sorted_data) + 1) / len(sorted_data)
return sorted_data, cdf
xlabel = label_dict[target_col]['x']
ylabel = label_dict[target_col]['y']
# Plot 1: RMSE/MAE across attribute sets
attr_fig, best_attr_set = _plot_attribute_order_line()
# attr_fig = _plot_attribute_order_cdf()
plots.append(attr_fig)
# Plot 2: Actual vs Predicted for best set
best_attr = [e for e in results_df.keys() if e.endswith(best_attr_set)][0]
best_result = results_df[best_attr]['oos_predictions']
sfig, median_trial = _plot_scatter_with_regression(best_result, xlabel, ylabel, target_col)
plots.append(sfig)
# Plot 3: Convergence plot
convergence_df = results_df[best_attr]['convergence']
cfig = _plot_convergence(convergence_df, median_trial)
plots.append(cfig)
# Plot 4: CDFs
cdf_arrays = []
for i, grp_result in results_df[best_attr]['oos_predictions'].groupby('fold'):
sorted_data, cdf = _compute_empirical_cdf(grp_result['actual'].values)
cdf_arrays.append((sorted_data, cdf))
cdffig = _plot_target_cdfs(cdf_arrays, xlabel)
plots.append(cdffig)
return plots
In the sequence of plots below, we change the order that groups of attributes are added to training.
We split the CF folds using a stratified approach to balance the target variable distribution in each fold (right-most plot).
The plot 3rd from left shows the objective score at each iteration to show how the training and test sets compare. We don’t want to continue training when the test sets are not improving.
n = 0
all_plots = []
for c in target_cols:
data = group_results_dict[c][n]
eval_metric = eval_metrics[loss]
grp_plots = create_results_plots(c, data['results'], data['order'], eval_metric)
all_plots += grp_plots
layout = gridplot(all_plots, ncols=4, width=300, height=275)
show(layout)
Min prediction risk occurs at the maximum iteration, try increasing the number of boosting rounds
Min prediction risk occurs at the maximum iteration, try increasing the number of boosting rounds
n = 3
all_plots = []
for c in target_cols:
data = group_results_dict[c][n]
eval_metric = eval_metrics[loss]
grp_plots = create_results_plots(c, data['results'], data['order'], eval_metric)
all_plots += grp_plots
layout = gridplot(all_plots, ncols=4, width=300, height=275)
# show(layout)
n = 2
all_plots = []
for c in target_cols:
data = group_results_dict[c][n]
eval_metric = eval_metrics[loss]
grp_plots = create_results_plots(c, data['results'], data['order'], eval_metric)
all_plots += grp_plots
layout = gridplot(all_plots, ncols=4, width=300, height=275)
show(layout)
Min prediction risk occurs at the maximum iteration, try increasing the number of boosting rounds
Min prediction risk occurs at the maximum iteration, try increasing the number of boosting rounds
n = 1
all_plots = []
for c in target_cols:
data = group_results_dict[c][n]
eval_metric = eval_metrics[loss]
grp_plots = create_results_plots(c, data['results'], data['order'], eval_metric)
all_plots += grp_plots
layout = gridplot(all_plots, ncols=4, width=300, height=275)
# show(layout)
Min prediction risk occurs at the maximum iteration, try increasing the number of boosting rounds
Test the sensitivity to Order of attribute groups#
Note that in the first plot (at left) the attribute groups are additive. That is, the GBM is trained on just the first group listed in the categorical x-axis, then the second group attributes are added to the first, then the third group is added to the first and second, and so forth.
Test randomly permuted target values#
As a last iteration, randomize the order of the mean_runoff column to test what the algorithm is learning.
The predictive power decreases substantially across all groupings of input attributes.
random_results = {}
group_order = group_1
for tc in target_cols:
print(f'Processing randomization for target column: {tc}')
test_results_fname = f'{tc}_prediction_results_shuffled.npy'
test_results_fpath = os.path.join(results_folder, test_results_fname)
if os.path.exists(test_results_fpath):
shuffled_test_results = np.load(test_results_fpath, allow_pickle=True).item()
else:
shuffled_df = filtered_df.copy()
for attr in all_attributes:
# randomly shuffle the order of attribute values
attr_values = filtered_df[attr].values
np.random.shuffle(attr_values)
shuffled_df[attr] = attr_values
shuffled_test_results = predict_runoff_from_attributes(shuffled_df, tc, group_order, results_folder, n_boost_rounds, n_optimization_rounds, loss)
np.save(test_results_fpath, shuffled_test_results)
random_results[tc] = {'order': group_order, 'results': shuffled_test_results}
Processing randomization for target column: uar_mean
Processing randomization for target column: uar_std
Processing randomization for target column: uar_median
Processing randomization for target column: uar_mad
Processing randomization for target column: log_uar_mean
Processing randomization for target column: log_uar_std
Processing randomization for target column: log_uar_median
Processing randomization for target column: log_uar_mad
View results of shuffled target variable (mean runoff)#
all_shuffled_plots = []
for tc in target_cols:
shuffled_results = random_results[tc]['results'].copy()
group_order = random_results[tc]['order']
shuffled_runoff_plots = create_results_plots(tc, shuffled_results, group_order, eval_metric, title='')
all_shuffled_plots += shuffled_runoff_plots
layout = gridplot(all_shuffled_plots, ncols=4, width=300, height=275)
# show(layout)
# process the results into a dictionary object for easy access to predicted values
median_predictions = []
for tc in target_cols:
group_results = group_results_dict[tc]
# just pick the first test, ['climate', '+terrain', '+land_cover', '+soil']
# and pick the '+land_cover' set
group_data = group_results[0]
# print(group)
# evaluate on climate + terrain + land_cover set (neglect soil)
data = group_data['results']['+land_cover']
all_tests_df = data['all_results']
# get the MEDIAN predicted value from all trials as a list for each station (more robust than mean)
all_station_median_predictions = data['oos_predictions'][['official_id', 'predicted']].groupby('official_id').agg(lambda x: np.percentile(x, 50))#.tolist()
actual_value = data['oos_predictions'][['official_id', 'actual']].groupby('official_id').agg(list)
actual_value = actual_value['actual'].apply(lambda x: list(set(x))) # all actual values are the same for a given station
# assert all actual value lists are length 1
assert np.all(actual_value.apply(lambda x: len(x) == 1)), f"Not all actual value lists are length 1 for target column {tc}"
actual_value = actual_value.apply(lambda x: x[0]).to_dict() # extract the single value from the list
all_station_median_predictions['actual'] = all_station_median_predictions.index.map(actual_value)
# rename and aggregate per site (in case multiple rows per official_id remain)
all_station_median_predictions.rename(columns={
'predicted': f'{tc}_predicted',
'actual': f'{tc}_actual'
}, inplace=True)
median_predictions.append(all_station_median_predictions)
median_predictions_df = pd.concat(median_predictions, axis=1)
median_predictions_df.reset_index(inplace=True)
median_predictions_df.to_csv(os.path.join(results_folder, 'OOS_parameter_predictions.csv'), index=False)
from scipy.stats import linregress
plots = []
for pred_label, obs_label in [('uar_mean_predicted', 'uar_mean_actual'), ('uar_std_predicted', 'uar_std_actual'),
('uar_median_predicted', 'uar_median_actual'), ('uar_mad_predicted', 'uar_mad_actual'),
('log_uar_mean_predicted', 'log_uar_mean_actual'), ('log_uar_std_predicted', 'log_uar_std_actual'),
('log_uar_median_predicted', 'log_uar_median_actual'), ('log_uar_mad_predicted', 'log_uar_mad_actual'),
]:
y, x = median_predictions_df[pred_label], median_predictions_df[obs_label]
f = figure(title=f'{obs_label} vs. {pred_label}', width=400, height=400)
f.scatter(x, y, size=2, color='black', alpha=0.5)
# compute regression line using linregress
slope, intercept, r_value, p_value, std_err = linregress(x, y)
x_fit = np.array([x.min(), x.max()])
y_fit = intercept + slope * x_fit
f.line(x_fit, y_fit, line_color='red', line_width=2, line_dash='dashed',
legend_label=f'y={slope:.2f}x+{intercept:.2f}, R²={r_value**2:.2f}')
f.xaxis.axis_label = obs_label
f.yaxis.axis_label = pred_label
plots.append(f)
lt = gridplot(plots, ncols=4, width=350, height=300)
show(lt)
Discussion#
Reordering the attribute groupings suggests there are interactions between attributes in model training.
Across all orderings, the climate attributes provide most predictive information,
Soil attributes contribute little or no explanatory power to the model.
Terrain and land cover attributes provide some predictive information over soil, but the joint entropy with climate seems to represent much of this information gain,
Randomly permuting the order of the target variable,
mean_runofferases all predictive power.